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Maximum Likelihood Estimation
Maximum Likelihood Estimation
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Why do we maximize the log-likelihood instead of the likelihood directly in maximum likelihood estimation?
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A.
The log turns products of probabilities into sums, which is numerically stable and easier to optimize
B.
The likelihood function is always negative for real-valued data, so taking the log transforms it to a positive quantity
C.
Applying the logarithm always makes the resulting objective function convex, guaranteeing a unique global maximum
D.
The log-likelihood and the likelihood have different maximizers, and the log-likelihood maximizer is statistically superior
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